Remarks on derived complete modules and complexes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00569849" target="_blank" >RIV/67985840:_____/23:00569849 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1002/mana.202000140" target="_blank" >https://doi.org/10.1002/mana.202000140</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.202000140" target="_blank" >10.1002/mana.202000140</a>

Result language
angličtina
Original language name
Remarks on derived complete modules and complexes
Original language description
Let R be a commutative ring and I a finitely generated ideal in R. We discuss two definitions of derived I-adically complete (also derived I-torsion) complexes of R-modules which appear in the literature: the idealistic and the sequential one. The two definitions are known to be equivalent for a weakly proregular ideal I, we show that they are different otherwise. We argue that the sequential approach works well, but the idealistic one needs to be reinterpreted or properly understood. We also consider I-adically flat R-modules.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA20-13778S" target="_blank" >GA20-13778S: Symmetries, dualities and approximations in derived algebraic geometry and representation theory</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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